Here’s a case for talent poaching: When people jump from one company to a rival firm, they feel more competitive with their former employer than their new co-workers do, finds a new study in the Academy of Management Journal.

Employees form attachments with a company over time, and associate a part of their identity with the group they work with, the study explains. To prove their loyalty to their new firm, switchers tend to become overly aggressive toward their former employers.

But be warned: That competitive feeling doesn’t extend to individual former-colleagues. According to study author Thorsten Grohsjean, the lesson to companies looking to poach a superstar from the competition is that “it is a better idea to poach whole teams rather than individuals.”

If you only intend to lure one person over to your side, don’t pit them directly against former colleagues; that just stresses them out and harms job performance.